Nucleoside analogues have played a pivotal role in the treatment of hematological malignancies. While the first analogue was used more than 50 years ago, during the last five years, four new congeners were approved for therapy. A common feature among these clinically used analogues is that they are all DNA-directed;analogues that are exclusively affecting RNA have not been brought to the clinic. 8-chloro-adenosine is a novel and unique nucleoside analogue that is first in its class to be tested in the clinic. First, in contrast to other clinically used analogues, this agent has a ribose sugar. Second, 8-Cl-Ado is phosphorylated by adenosine kinase which is present in high specific activity in cancer cells as opposed to deoxycytidine kinase which activates currently used analogues. Third, 8-chloro-adenosine triphosphate (8-Cl-ATP) is incorporated into RNA without any effect on DNA synthesis. Fourth, 8-Cl-ATP is also incorporated into poly(A) tail of transcripts resulting in inhibition of polyadenylation and mRNA synthesis. As a consequence of the actions on mRNA synthesis, there is a depletion of short-lived transcripts. Fifth, biochemical studies and molecular modeling data have suggested that 8-chloro-adenosine diphosphate (8-Cl-ADP) is a substrate and 8-Cl-ATP is an inhibitor for mitochondrial ATP synthase, the apical enzyme of the oxidative phosphorylation pathway which results in a depletion of cellular bioenergy. Collectively these features make this analogue a first in its class. Based on this background, the investigators hypothesized that 8-Cl-Ado will elicit novel pharmacodynamic responses to non-growing or indolent malignant cells. The investigators state that the uniqueness of 8-Cl-Ado was recognized by peers in this field as they have obtained two awards from the National Cancer Institute, an investigational drug application (IND) from the Food and Drug Administration, and drug material to conduct their Phase 1 clinical investigation in patients with CLL. To achieve their overall goal and to test their hypothesis, the investigators plan to pursue the following three aims. Aim 1. Using established guidelines evaluate toxicity of 8-Cl-Ado. Conduct the Phase 1 clinical trial in subjects with CLL to determine the hematological and nonhematological toxicity profile and identify the MTD and DLT. Aim 2. Using established guidelines evaluate efficacy of 8-Cl-Ado. Conduct the Phase 1 clinical trial in subjects with CLL to determine the clinical benefits of the drug. Determine complete remission, partial remissions, and hematological improvements. Aim 3. Using well-defined biomarkers, evaluate pharmacokinetics and pharmacodynamics of 8-Cl-Ado during Phase 1/2 clinical trial in patients with CLL. The investigators state that these Aims will establish utility of 8-Cl-Ado in CLL, provide a dose for Phase 2 study, and knowledge for optimal use of this agent alone and in combination.